by JLS
for the Grice Club.
WE HAVE SEEN that Moore is taking issue with Russell. Further down in the 1919 essay, Moore is more explicit about this:
"Mr. Russell, in the Principles of Mathematics (p. 34), treats the phrase, "q can be deduced from p" as if it meant exactly the same thing as "p ) q", or "p materially implies q"; and has repeated the same error elsewhere, e.g. in Philosophical Essays (p. 166). ... 'p ent q' does not mean the same as 'p ) q'".
Moore goes on to quote Strachey (Mind) on Lewis on "p strictly implies q". (The distinction Moore claims is ignored by Whitehead's and Russell's Principia (Moore quotes from p. 21 of PM as an illustration).
Moore's rebuttal:
"The proposition that I am in this room does materially
imply that I am more than five years old, since both
are true; and the assertion that it does is ... an
instance of a true formal implication, since it is in
fact true that all persons in this room are more
than five years old; but nothing appears to me then [sic]
the second of these two propositions can NOT be
deduced from the first -- that the kind of relation
which holds between the premisses, and conclusion of
a syllogism in Barbara does NOT hold between them. To
put it another way, it seems to me quite obvious
that the properties, "being a person in this room"
and "being more than five years old" are NOT related
in any kind of way in which "being a right angle" is
related to "being an angle", and which we express by
saying that, in the case of every term, the proposition
that the term is an angle can be deduced from the
proposition that the term is a right angle."
----
Note that this involves Grice's 'disimplicature' into the bargain.
"I brouhgt some flowers!"
--- "You did not! They are PLASTIC flowers!"
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Though Moore is correct in his critique there is a defence of Russell in the context of the formalisation of mathematics.
ReplyDeleteSo long as your deductive system contains no contingent axioms and the rules are all logically sound, all the theorems of the form p=>q establish the analyticity of p=>q, and it is then the case that p semantically entails q.
RBJ
Good. The thing is actually online, and I was just moved to revisit due to commentary by R. Paul publicly elsewhere. In between these segments, Moore does mention Leibniz, and the self-evident, and the apodeictic and the 'necessary truth', which I thought you would enjoy -- if only for your debate with Bayne on this matters in Hist-Analytic!
ReplyDeleteI should re-read the whole Moore thing, and I trust Grice never paid him the undue credit! But Moore's main example, it seems, seems to be indeed with
'x is red' entails 'x is coloured'.
This Moore does not necessarily distinguish from his OTHER example:
"x is a right angle" entails "x is an angle"
But Wang would have the first as SEMANTIC entailment (there is NOTHING in 'coloured' that says "RED") while the second as a more primitive, logical soundER syntactic entailment (with Grice's provisos: "HMS Pinafore sank the Bismark" does NOT entail "HMS Pinafore sank").
In any case, it's all about the apriori, etc. and Descartes and Leibniz on things that only Kant thought he understood. Recall at this point Grice's example of the 'synthetic a priori' -- in a draft for his WoW, now in Grice Papers, Bancroft Library --
"Nothing can be red and green all over".
and how he would tease children about this. He possibly DOUBTED if it was not just 'analytic' rather than 'synthetic a priori' as Kant thought.
It may do to revise the exact quote for Strachey in "Mind" (Moore edited Mind, so he would know) where Moore says Strachey attempts to improve on Russell (without success) via Lewis. To think this was already in the proceedings back in the day (1919) IS moving, even if Cantabrigensis!